A bracket sequence is a string that is one of the following:
- An empty string;
- The concatenation of (, A, and ) in this order, for some bracket sequence A ;
- The concatenation of A and B in this order, for some non-empty bracket sequences A and B /
Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

-----Constraints-----
- $1 \leq N \leq 10^6$
- The total length of the strings S_i is at most 10^6.
- S_i is a non-empty string consisting of ( and ).

-----Input-----
Input is given from Standard Input in the following format:
N
S_1
:
S_N

-----Output-----
If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

-----Sample Input-----
2
)
(()

-----Sample Output-----
Yes

Concatenating (() and ) in this order forms a bracket sequence.

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